A231753 T(n,k)=Number of nXk 0..2 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors

3, 3, 3, 9, 15, 9, 22, 51, 51, 22, 51, 186, 589, 186, 51, 121, 687, 5106, 5106, 687, 121, 292, 2485, 41288, 101517, 41288, 2485, 292, 704, 9068, 397219, 1787168, 1787168, 397219, 9068, 704, 1691, 33308, 3745096, 36596191, 67411714, 36596191, 3745096

Offset

1,1

Comments

Table starts

....3......3..........9............22................51................121

....3.....15.........51...........186...............687...............2485

....9.....51........589..........5106.............41288.............397219

...22....186.......5106........101517...........1787168...........36596191

...51....687......41288.......1787168..........67411714.........2966010838

..121...2485.....397219......36596191........2966010838.......309458955366

..292...9068....3745096.....764681711......131956285636.....31638510266609

..704..33308...34036486...15421779553.....5669387332934...3041193156650724

.1691.121445..313782748..309633476778...243573416110820.296576264769131499

.4059.444183.2927905037.6284893573378.10555475178328001

Links

R. H. Hardin, Table of n, a(n) for n = 1..112

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5) for n>6

k=2: [order 11]

k=3: [order 40] for n>41

Example

Some solutions for n=4 k=4
..1..0..1..1....1..0..0..0....2..0..0..2....2..2..0..0....0..0..2..2
..0..0..0..2....0..0..0..1....1..0..0..0....1..0..0..0....0..1..0..0
..0..0..1..0....1..0..0..1....2..0..0..0....0..1..0..0....2..0..0..0
..1..0..0..0....1..0..0..0....2..1..0..0....0..0..0..1....2..0..0..0

Crossrefs

Column 1 is A202882 for n>1

Sequence in context: A161808 A188344 A217457 * A231663 A180439 A298315

Adjacent sequences: A231750 A231751 A231752 * A231754 A231755 A231756

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2013

Status

approved